If x= 1+ cube root of 2 + cube root of 4, find (1+1/x)^3?

Question

Please show me complete working. Good luck in solving this. Please tell me a maths website where I can find these kind of questions with answers.

Answer 1

x = 1 + ³√2 + ³√4 = 1 + ³√2 + (³√2)²

Noting that a³ - 1 = (a - 1) (a² + a + 1)

So (³√2 - 1)(³√2)² + ³√2 + 1) = (³√2)³ - 1 = 1

1/x = 1/(1 + ³√2 + (³√2)² ) * (³√2 - 1)/(³√2 - 1)
= (³√2 - 1)/[(³√2)³ - 1]
= (³√2 - 1)

So (1 + 1/x)³ = (1 + ³√2 - 1)³ = 2

Answer 2

1 + Cube Root of 2 + Cube Root of 4 = 3.847322102

x = 2

Answer 3

let a=1
b=cube root of 2 + cube root of 4
(1+1/x)^3=(1+x)^3/x^3
1+x=2+cube root of 2 + cube root of 4

expand both numerator and denominator

Numerator=38 + 30*2^(1/3) + 20*4^(1/3)
Denominator=19 + 15*2^(1/3) + 10*4^(1/3)

Thus anwser is 2.

Answer 4

Given
x = 1 + 2^(1/3) + 4^(1/3)
x = 1 + 2^(1/3) + 2^(2/3)

Let y = (1 + 1/x)^3

y = (1 + 1/x)^3
= [1 + 1/(1 + 2^(1/3) + 2^(2/3))]^3
= [(1 + 2^(1/3) + 2^(2/3) + 1)/(1 + 2^(1/3) + 2^(2/3))]^3
= [(2^(1/3) + 2^(2/3) + 2)/(1 + 2^(1/3) + 2^(2/3))]^3
= [2^(1/3)(1 + 2^(1/3) + 2^(2/3))/(1 + 2^(1/3) + 2^(2/3))]^3
= 2^(1/3)^3 = 2

Answer 5

f(x) = dice root (x² - a million) f(x) = (x² - a million)^(a million/3) Use the chain rule -- initiate on the outdoors with the a million/3 exponent and use the flexibility rule (said decrease than) Then multiply that by the spinoff of the interior (x² - a million) f'(x) = a million/3 * (x² - a million)^(-2/3) * (2x) f'(x) = (2x)/(3((x² - a million)^(2/3))) --------------------- in addition, f(x) = 12 * x^(a million/4) f'(x) = 12 * (a million/4) * x^(-3/4) f'(x) = 3/x^(3/4)

Answer 6

let 2^(1/3) = y

x = 1 + y + y^2 = (y^3-1)/(y-1) = (2-1)/(y-1) = 1/(y-1)

1/x = y-1

(1+1/x) = y

(1+1/x)^3 = y^3 = 8

Answer 7

x(2^(1/3)-1) = (2^(2/3)+2^(1/3)+1)(2^(1/3)-1) = [2^(1/3)]^3- 1
=2-1 = 1
Thus, 1/x = 2^(1/3)-1
meaning that 1+1/x = 2^(1/3)

or that (1+1/x)^3 = 2.

So it is 2.

Answer 8

x=1+1.3+1.6=3.9
1+1/3.9=4.9/3.9
4.9/3.9*3=14.7/3.9
is that all right?